IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v8y2020i3p72-d379252.html
   My bibliography  Save this article

Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk

Author

Listed:
  • Jingnan Wang

    (Department of Mathematics, University of Kaiserslautern, 67663 Kaiserslautern, Germany)

  • Ralf Korn

    (Department of Mathematics, University of Kaiserslautern, Fraunhofer ITWM, 67663 Kaiserslautern, Germany)

Abstract

We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce two main algorithms, a discrete penalization scheme and a discrete reflected scheme basing on a random walk approximation of the Brownian motion as well as a discrete approximation of the default martingale, and we study these two methods in both the implicit and explicit versions respectively. We give the convergence results of the algorithms, provide a numerical example and an application in American game options in order to illustrate the performance of the algorithms.

Suggested Citation

  • Jingnan Wang & Ralf Korn, 2020. "Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk," Risks, MDPI, vol. 8(3), pages 1-30, July.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:72-:d:379252
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/8/3/72/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/8/3/72/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/5717 is not listed on IDEAS
    2. Francesco Cordoni & Luca Di Persio, 2014. "Backward Stochastic Differential Equations Approach to Hedging, Option Pricing, and Insurance Problems," International Journal of Stochastic Analysis, Hindawi, vol. 2014, pages 1-11, September.
    3. Shige Peng & Xiaoming Xu, 2009. "BSDEs with random default time and their applications to default risk," Papers 0910.2091, arXiv.org.
    4. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    5. Hamadène, S. & Lepeltier, J. -P., 2000. "Reflected BSDEs and mixed game problem," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 177-188, February.
    6. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    7. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
    8. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    2. Fahrenwaldt, Matthias Albrecht & Jensen, Ninna Reitzel & Steffensen, Mogens, 2020. "Nonrecursive separation of risk and time preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 95-108.
    3. Dirk Becherer & Wilfried Kuissi-Kamdem & Olivier Menoukeu-Pamen, 2023. "Optimal consumption with labor income and borrowing constraints for recursive preferences," Working Papers hal-04017143, HAL.
    4. Dominika Czyz & Karolina Safarzynska, 2023. "Catastrophic Damages and the Optimal Carbon Tax Under Loss Aversion," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 85(2), pages 303-340, June.
    5. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    6. Huang, Jianhui & Wang, Guangchen & Wu, Zhen, 2010. "Optimal premium policy of an insurance firm: Full and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 208-215, October.
    7. Chabakauri, Georgy, 2010. "Asset pricing with heterogeneous investors and portfolio constraints," LSE Research Online Documents on Economics 43142, London School of Economics and Political Science, LSE Library.
    8. Riedel, Frank, 2005. "Generic determinacy of equilibria with local substitution," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 603-616, August.
    9. Li, Hanwu & Riedel, Frank & Yang, Shuzhen, 2024. "Optimal consumption for recursive preferences with local substitution — the case of certainty," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    10. Marc Arnold & Dirk Hackbarth & Tatjana Xenia Puhan, 2018. "Financing Asset Sales and Business Cycles [Does industry-wide distress affect defaulted firms? Evidence from creditor recoveries]," Review of Finance, European Finance Association, vol. 22(1), pages 243-277.
    11. Miyoshi, Yoshiyuki & Toda, Alexis Akira, 2017. "Growth effects of annuities and government transfers in perpetual youth models," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 1-6.
    12. Ruan, Xinfeng, 2021. "Ambiguity, long-run risks, and asset prices in continuous time," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 115-126.
    13. Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
    14. Frederick Ploeg, 2021. "Carbon pricing under uncertainty," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 28(5), pages 1122-1142, October.
    15. Shi, Huihong & Mu, Congming & Yang, Jinqiang & Huang, Wenli, 2021. "A Sino-US comparative analysis of the hi-tech entrepreneurial model," Economic Modelling, Elsevier, vol. 94(C), pages 953-966.
    16. Camelia Minoiu & Andrés Schneider & Min Wei, 2023. "Why Does the Yield Curve Predict GDP Growth? The Role of Banks," FRB Atlanta Working Paper 2023-14, Federal Reserve Bank of Atlanta.
    17. Zixin Feng & Dejian Tian, 2021. "Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints," Papers 2111.09032, arXiv.org, revised May 2023.
    18. Emmanuelle Augeraud-Véron & Giorgio Fabbri & Katheline Schubert, 2019. "The Value of Biodiversity as an Insurance Device," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 101(4), pages 1068-1081.
    19. Joshua Lanier & Bin Miao & John K.-H. Quah & Songfa Zhong, 2024. "Intertemporal Consumption with Risk: A Revealed Preference Analysis," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1319-1333, September.
    20. Kraft, Holger & Weiss, Farina, 2019. "Consumption-portfolio choice with preferences for cash," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 40-59.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:72-:d:379252. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.